# Stage 121 — Sensitivity to capital response and investment closure

## Result

Of **324 policy cases**, **257 qualify as successes**, **27 complete but fail the funding/consumption gates**, and **40 halt**. Eleven of twelve no-policy controls complete. Halted paths and failed controls are never counted as successful twenty-year comparisons.

Of the 257 successes, **149 pay positive supplemental grants** and **108 meet the floor without grants**. A no-grant success is not credited to redistribution.

| Capital elasticity | All residual investment productive | Productive investment = 5% of output | Productive investment = 7.5% of output |
| --- | ---: | ---: | ---: |
| 0 | 18 / 27 | 18 / 27 | 8 / 27 |
| 0.15 | 27 / 27 | 24 / 27 | 27 / 27 |
| 0.30 | 27 / 27 | 27 / 27 | 27 / 27 |
| 0.45 | 0 / 27 | 27 / 27 | 27 / 27 |

Entries are qualified successes among the 27 floor/response/ceiling combinations in each cell, not estimated probabilities. The 0.45/residual control itself fails in year 20 from corporate cash exhaustion; its 27 policy paths also halt. These are failures of the declared model closure, not forecasts of corporate default.

## What changed

The experiment inherits stage 120's annual current-need, funding-limited grants. It varies the capital-output elasticity over 0, 0.15, 0.30 and 0.45, and compares three productive-investment rules.

In the original residual rule, net investment equals output less household consumption, housing upkeep and existing government goods, and all investment becomes productive capital.

In the two planned rules, productive investment targets 5% or 7.5% of current output. The difference between total residual investment and productive investment becomes inventory investment. This inventory account closes the goods identity:

**Output = nonhousing consumption + housing upkeep + government goods + productive investment + inventory change.**

Corporate cash finances **total** investment, including inventory change; financing only productive investment would leave the monetary identity incomplete. Future production responds only to productive capital.

Every path starts with zero real inventory. Inventory may accumulate or be drawn down but cannot become negative. A proposal requiring negative inventory halts before that annual state is committed. Inventory is assumed nonproductive, without carrying cost or depreciation. This is an alternative declared closure, not an estimated investment demand equation.

## Failure decomposition

- 13 policy cases halt because planned productive investment plus consumption requires more goods than current production and available inventory permit.
- 27 halt from the inherited corporate liquidity/capital/equity-capacity constraint; in this grid the recorded cause is negative corporate cash in the high-elasticity residual configuration.
- 27 complete but do not fully finance current grant requests and do not preserve both consumption floors.

There are no incomplete paths silently shortened and then reported as preservation successes. A policy outcome cannot qualify if its matched control fails. Terminal policy/control differences are withheld for incomplete pairs.

An inventory failure means the specified fixed-price, fixed-rule system cannot accommodate all demands. It does not prove that a real economy would fail: prices, investment plans or other adjustment mechanisms might change, but those mechanisms are not present here.

## Design and comparability

There are four elasticities × three investment rules × three floors (90%, 95%, 100%) × three owner responses (0, 0.5, 1) × three dividend ceilings (5%, 10%, 20%) = 324 policy cases, with twelve matched controls.

Each reference is the first completed annual observation of the same rule/elasticity no-policy control. It is not taken from a policy path or a pre-automation observation. Existing employment and price schedules remain external.

The current grant request separately covers desired-spending and cash/equity-resource constraints. The actual grant is limited by a dividend-based owner levy and cash. Unfunded current need is recorded rather than converted into an unconditional entitlement. No monthly timing claim is made.

The elasticity/rule grid is illustrative and uncalibrated. It is not a probability distribution over possible economies. The exercise changes productive allocation and explicitly accounts for inventory; it does not establish robustness to every alternative macroeconomic closure.

## Validation and reproduction

Six tests verify exact recovery of the prior residual engine, money/goods/capital/inventory identities, actual application of planned productive investment, exclusion of halted policies and failed controls, grid/funding gates, and archive reproduction.

```sh
python scripts/investment_closure_sensitivity_v121.py --output data/processed/investment_closure_sensitivity_v121.json
python scripts/test_investment_closure_sensitivity_v121.py
```

[All cases, controls and failure records](data/processed/investment_closure_sensitivity_v121.json) retain annual state rows under the explicit row_columns schema. Full records can be reproduced with simulate_households(). Original simulator files are unchanged. Repository CI remains the merge gate.

## Research implication and next step

The central result is conditional: financing a consumption floor and sustaining the productive path are separate requirements. Some apparent successes do not require redistribution, while other paths fail through goods or corporate cash constraints.

Next trace the two failure channels through a small set of matched annual accounts: whether insufficient inventories arise from a rigid productive-investment target, and whether corporate cash failure arises from the equity-financing rule. Explain these mechanisms before expanding scenarios or treating the success count as evidence for the thesis.